# broadband least-squares wave-equation migration - · pdf filebroadband least-squares...

Post on 19-Mar-2018

214 views

Embed Size (px)

TRANSCRIPT

Broadband Least-Squares Wave-Equation Migration

Shaoping Lu*, Xiang Li, A.A. Valenciano, Nizar Chemingui (PGS) and Cheng Cheng (UC-Berkeley)

Summary

In general, Least-Squares Migration (LSM) can produce

images corrected for overburden effects, variations in

illumination, and incomplete acquisition geometry. The

modeling engine of our LSM implementation consists of a

visco-acoustic anisotropic one-way wave-equation

extrapolator. It has the advantage of efficiently propagating

high-frequency seismic data using high-resolution earth

models (e.g. derived from Full Waveform Inversion).

Applications to synthetic and field data examples (from the

Gulf of Mexico and the North Sea) consistently delivered

higher resolution images with better amplitude balance

when compared to standard seismic migration.

Introduction

Depth migration produces a blurred representation of the

earth reflectivity, with biased illumination and limited

wavenumber content. The image resolution at a given depth

is controlled by the migration operators, the acquisition

parameters (source signature, frequency bandwidth,

acquisition geometry), and the earth properties at the

reflector depth and the overburden (velocity, attenuation).

Some of these conditions can be mitigated during

acquisition and processing by employing technologies like:

multi-sensor data, full azimuth acquisition geometries,

deghosting, attenuation compensation and using high-

resolution earth models during depth migration (i.e. models

derived from Full Waveform Inversion). However, when

heterogeneities are present in the earth and the acquisition

geometry leads to insufficient source and receiver coverage

on the surface, both the illumination and wavenumber

content of the depth-migrated images can be significantly

restricted.

The resolution of the depth images can be improved by

posing the imaging problem in terms of least squares

inversion. The Least-Squares Migration (LSM) solutions

(Schuster, 1993; Nemeth et al., 1999; Prucha and Biondi,

2002) are designed to produce images of the subsurface

corrected for wavefield distortions caused by acquisition

and propagation effects. They implicitly solve for the earth

reflectivity by means of data residual reduction in an

iterative fashion, which usually demands intensive

computation. In seismic exploration framework, Nemeth et

al. (1999) derived a Least-Squares Migration following a

high-frequency Kirchhoff integral asymptotic

approximation (ray-based). Later, Prucha and Biondi

(2002) derived less restrictive broadband wave equation

solutions. The advantage of broadband wave-equation

extrapolators is that they make better use of the high-

resolution earth models derived with advanced processing

technologies such as Full Waveform Inversion FWI

(Korsmo et al., 2017).

Here, we implement an LSM using an accurate visco-

acoustic anisotropic one-way wave-equation operator

(Valenciano et al., 2011). Our application integrates the

one-way operator with a fast linear inversion solver in an

efficient migration/demigration workflow, namely a Least-

Squares one-way Wave-Equation Migration (LS-WEM).

Applications of LS-WEM to both synthetic and field data

examples improve images amplitude balance and enhance

both temporal and spatial resolution.

Methodology

Seismic migration is the adjoint solution to the forward

modeling problem:

m = LT

dobs (1)

where, dobs is the observed data , L represents the linearized

(Born) modeling operator, and its adjoint LT is the

migration operator. However, the heterogeneity of the

overburden and/or limitations of the acquisition geometry

can affect the illumination and wavenumber content of the

estimated image m.

A better approximation of the earth reflectivity is obtained

by using a least squares inversion, which solves a

minimization problem to approximate the true reflectivity

m as:

m = argminm || dobs Lm ||2

2 (2)

In this case, the acquisition geometry, which relates to the

operator L, has less effect to the resulting image m.

Here we introduce an implicit method to solve the Least-

Squares problem. The LSM simulates data by wave-

equation Born modeling, and iteratively updates the

reflectivity by migration of the misfits between the

observed and simulated data. The algorithm can be

summarized by the diagram in Figure 1 using an iterative

modeling/migration framework. The first step of the flow is

to produce an approximate reflectivity (migration). In the

next step, the reflectivity is used in Born modeling. When

the data residual || dobs - dmod || is large, it is migrated to

update the image m. The inversion converges when the

simulated data matches the observation. One iteration (blue

loop in Figure 1) comprises one Born modeling and one

migration.

2017 SEG SEG International Exposition and 87th Annual Meeting

Page 4422

Dow

nloa

ded

09/1

5/17

to 2

17.1

44.2

43.1

00. R

edis

trib

utio

n su

bjec

t to

SEG

lice

nse

or c

opyr

ight

; see

Ter

ms

of U

se a

t http

://lib

rary

.seg

.org

/

Broadband Least-Squares Wave-Equation Migration

The computational cost of the iterative LSM relies on the

efficiency of the wavefield propagation algorithm. Here,

we implement the inversion using a one-way wave-

equation operator (Valenciano et al., 2011), which has

advantages of both accuracy and efficiency. In addition, our

implementation combines the one-way extrapolator with

fast linear inversion solvers into an efficient migration

inversion system.

Synthetic and field data examples

We have applied LS-WEM to the 2D Sigsbee2b synthetic

model [Figure 2]. The migration result [Figure 2A] shows

uneven illumination from left sedimentary to subsalt area,

including shadow zones related to the complex salt

structures. LS-WEM improves the illumination by

balancing the image amplitudes and reducing the effects of

the shadow zones [Figure 2B]. LS-WEM also enhances

temporal resolution by broadening the frequency spectrum

[Figure 2E]. Figure 2C and 2D show that LS-WEM

balances the wavenumber content and improves the image

of the faults and dipping salt flacks (indicated by arrows).

Figure 1: An iterative LSM algorithm solves for the earth

reflectivity m. It simulates synthetic data dmod by using a

Born modeling operator, and iteratively update the

reflectivity image m using migration of the data residual

||dobs - dmod||.

In addition, LS-WEM converges rapidly to the true

solution, reducing the data residuals by 90% in only four

iterations [Figure 2F].

Figure 2: Sigsbee2b 2D synthetic example: (A) WEM image; (B) LS-WEM image; (C) F-K spectrum of WEM; (D) F-K spectrum

of LS-WEM; (E) Frequency spectra of WEM [red] and LS-WEM [blue]; (F) LS-WEM objective function convergence rate.

WEM

(A)

Least-Squares WEM

(B)

2017 SEG SEG International Exposition and 87th Annual Meeting

Page 4423

Dow

nloa

ded

09/1

5/17

to 2

17.1

44.2

43.1

00. R

edis

trib

utio

n su

bjec

t to

SEG

lice

nse

or c

opyr

ight

; see

Ter

ms

of U

se a

t http

://lib

rary

.seg

.org

/

Broadband Least-Squares Wave-Equation Migration

Figure 3: Gulf of Mexico 3D WAZ field data example: (A) Depth slice at 1150m from WEM; (B) Depth slice at 1150m from LS-

WEM; (C) WEM F-K spectrum; (D) LS-WEM F-K spectrum; (E) Frequency spectra of WEM and LS-WEM.

Figure 4: Gulf of Mexico 3D WAZ field data example: Inline and xline images from (A) WEM and (B) LS-WEM.

9000m 15 km

0

(A) (B)

WEM Least-Squares WEM

2017 SEG SEG International Exposition and 87th Annual Meeting

Page 4424

Dow

nloa

ded

09/1

5/17

to 2

17.1

44.2

43.1

00. R

edis

trib

utio

n su

bjec

t to

SEG

lice

nse

or c

opyr

ight

; see

Ter

ms

of U

se a

t http

://lib

rary

.seg

.org

/

Broadband Least-Squares Wave-Equation Migration

We also applied the LS-WEM to a wide azimuth (WAZ)

data from the Gulf of Mexico. The results also demonstrate

that LS-WEM can deliver superior images compared to the

standard migration [Figure 3 and 4].

Figure 5: North Sea 3D NAZ field data example. Top:

WEM results; Bottom: LS-WEM results. The depth slice is

at 1.8km.

The image improvements of LS-WEM over the standard

migration can be summarized as: reduction of sail line

acquisition footprint (lateral stripes indicated by arrows in

Figure 3A), better resolution, and improved wavenumber

content [Figure 3C, 3D and 3E]. The inline images also